[nerdponx]

I just last night watched a mini-documentary on the origins of calculus in the work of Newton and Leibnitz, focusing specifically on how they came to be interested in the idea and their very earliest thoughts on it, often quoting directly from their notebooks.

The doc is on Youtube here: https://youtu.be/ObPg3ki9GOI

It was very clear that Newton in particular was building incrementally on work that other mathematicians had done before him. Leibniz was also making incremental improvements, but was apparently somewhat more visionary in his work. The Youtube comments are also interesting, including anecdotes of ancient Egyptian land surveyors using the same "sum of lines" technique (what Leibniz generalized into our modern antiderivative) in order estimate the areas of unevenly-shaped land plots along waterways for taxation.

Leibniz in particular was fascinating because it shows the incrementality of science continuing after him as well. Apparently Leibniz had built several computing machines, 150 years before Babbage, and was deliberately trying to work towards general and abstract paradigms for solving mathematical problems, 300 years before Hilbert, Church, Gödel, and Turing!